Math, asked by NewBornTigerYT, 10 months ago

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Answered by Anonymous

Question :

If ( 1 / p ) - ( 1 / q ) - ( 1 / q ) = 1 / 36 and pq + qr = pr, then find the value of r.

Solution :

Given :

$\implies \sf \dfrac{1}{p} - \dfrac{1}{q} - \dfrac{1}{r} = \dfrac{1}{36}$

Taking LCM

$\implies \sf \dfrac{ qr - pr - pq }{pqr} = \dfrac{1}{36}$

Substituting pr = pq + qr

$\implies \sf \dfrac{ qr - (pq + qr) - pq }{pqr} = \dfrac{1}{36}$

$\implies \sf \dfrac{ qr - pq - qr- pq }{pqr} = \dfrac{1}{36}$

$\implies \sf \dfrac{ - pq - pq }{pqr} = \dfrac{1}{36}$

$\implies \sf - \dfrac{2pq }{pqr} = \dfrac{1}{36}$

$\implies \sf - \dfrac{2}{r} = \dfrac{1}{36}$

$\implies \sf -2 \times 36 =r$

$\implies \sf r = - 72$

Therefore the value of r is - 72.

Answered by Equestriadash

$\bf Given:\ \sf \dfrac{1}{p}\ -\ \dfrac{1}{q}\ -\ \dfrac{1}{r}\ =\ \dfrac{1}{36};\ pq\ +\ qr\ =\ pr.\\\\\\\bf To\ find:\ \sf The\ value\ of\ r.\\\\\\\bf Answer:$

$\sf \dfrac{1}{p}\ -\ \dfrac{1}{q}\ -\ \dfrac{1}{r}\ =\ \dfrac{1}{36}\\\\\\\bf Taking\ its\ LCM\ and\ solving,\\\\\\\sf \dfrac{qr\ -\ pr\ -\ pq}{pqr}\ =\ \dfrac{1}{36}\\\\\\\bf \Big[pr\ =\ pq\ +\ qr\Big]\\\\\\\sf \dfrac{qr\ -\ (pq\ +\ qr)\ -\ pq}{pqr}\ =\ \dfrac{1}{36}\\\\\\\dfrac{qr\ -\ pq\ -\ qr\ -\ pq}{pqr}\ =\ \dfrac{1}{36}\\\\\\\dfrac{-2pq}{pqr}\ =\ \dfrac{1}{36}\\\\\\\dfrac{-2}{r}\ =\ \dfrac{1}{36}\\\\\\-72\ =\ r$

Therefore, r = - 72.

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Therefore the value of r is - 72.